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dE_logics Advocate
Joined: 02 Jan 2009 Posts: 2253 Location: $TERM

Posted: Sat Jun 22, 2013 7:18 am Post subject: What's 'permutation' in cryptography? 


If you believe the Internet it's long forgotten.
It's some undocumented procedure to juggle around bits of a block (for a block cipher), e.g. 
1,2,3,4,5,6,7,8,9,10 will juggle to 
3,5,2,7,4,10,1,9,8,6 _________________ My blog 

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John R. Graham Administrator
Joined: 08 Mar 2005 Posts: 10157 Location: Somewhere over Atlanta, Georgia

Posted: Sat Jun 22, 2013 11:02 am Post subject: 


It's not forgotten; it's just trivially weak, falling into the class called substitution ciphers. Any operation that has the property that, if you change one bit of the input, then exactly one bit of the output changes, is useless in cryptography. See also Ceaser Cipher.
 John _________________ I can confirm that I have received between 0 and 499 National Security Letters. 

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smartass Apprentice
Joined: 04 Jul 2011 Posts: 189 Location: right behind you ... (you did turn around, didn't you?)

Posted: Sat Jun 22, 2013 1:53 pm Post subject: 


Formally a permutation is a bijection (onetoone function) on the elements of {1 .. n } (set of numbers from 1 to n). The numbers 1 to n could be indices of some array of letter, bytes, etc.
As John has said, it's quite weak, but it's one of the building blocks of discrete mathematics which is used in cryptography, so that's why you might have come across it. 

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dE_logics Advocate
Joined: 02 Jan 2009 Posts: 2253 Location: $TERM

Posted: Sat Jun 22, 2013 3:14 pm Post subject: 


It's used in DES. That's why I needed it.
I'll see to Ceaser Cipher and revise sets.
But can someone link an article? _________________ My blog 

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John R. Graham Administrator
Joined: 08 Mar 2005 Posts: 10157 Location: Somewhere over Atlanta, Georgia

Posted: Sat Jun 22, 2013 3:32 pm Post subject: 


Not alone, but I think understand the ask a little better. It's because it's a well understood mathematical concept. (What is this "addition" that you speak of? Where is the instructional material?) DES was the first of a class of encryption algorithms called Feistel Ciphers. (An associate of mine was at IBM when Feistel invented it.) Wiki has some good material. In the context of DES, the PBoxes of each round of the DES algorithm rearrange the bits in an intermediate result block. Any rearrangement is a "permutation" and, in this context, that's all that it means. However, choosing the rearrangement pattern is part of the art of a good cipher, something I don't have the math to fully comprehend myself. (Cryptanalysis is a very narrow speciality and, although I'm a security architect, I'm a neophyte in that field.)
If you've got specific questions, go ahead & ask.
 John _________________ I can confirm that I have received between 0 and 499 National Security Letters.
Last edited by John R. Graham on Sat Jun 22, 2013 3:38 pm; edited 2 times in total 

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dE_logics Advocate
Joined: 02 Jan 2009 Posts: 2253 Location: $TERM

Posted: Sat Jun 22, 2013 3:33 pm Post subject: 


smartass wrote:  Formally a permutation is a bijection (onetoone function) on the elements of {1 .. n } (set of numbers from 1 to n). The numbers 1 to n could be indices of some array of letter, bytes, etc.
As John has said, it's quite weak, but it's one of the building blocks of discrete mathematics which is used in cryptography, so that's why you might have come across it. 
But in Simplified DES, what's the relation? _________________ My blog 

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John R. Graham Administrator
Joined: 08 Mar 2005 Posts: 10157 Location: Somewhere over Atlanta, Georgia

Posted: Sat Jun 22, 2013 3:42 pm Post subject: 


I'd never heard of Simplified DES but I imagine it has SBoxes and PBoxes, just like standard DES. (See my post just before your last one.)
 John _________________ I can confirm that I have received between 0 and 499 National Security Letters. 

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dE_logics Advocate
Joined: 02 Jan 2009 Posts: 2253 Location: $TERM

Posted: Sat Jun 22, 2013 4:00 pm Post subject: 


John R. Graham wrote:  Not alone, but I think understand the ask a little better. It's because it's a well understood mathematical concept. (What is this "addition" that you speak of? Where is the instructional material?) DES was the first of a class of encryption algorithms called Feistel Ciphers. (An associate of mine was at IBM when Feistel invented it.) Wiki has some good material. In the context of DES, the PBoxes of each round of the DES algorithm rearrange the bits in an intermediate result block. Any rearrangement is a "permutation" and, in this context, that's all that it means. However, choosing the rearrangement pattern is part of the art of a good cipher, something I don't have the math to fully comprehend myself. (Cryptanalysis is a very narrow speciality and, although I'm a security architect, I'm a neophyte in that field.)
If you've got specific questions, go ahead & ask. 
By now I've just 1 question left.
Taking this into reference 
http://elc.cu.edu.eg/elcmoodledata/90/moddata/scorm/288/01.htm
Are all permutation operations user function, or does the user/reader decide what permutations are to be made? _________________ My blog 

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John R. Graham Administrator
Joined: 08 Mar 2005 Posts: 10157 Location: Somewhere over Atlanta, Georgia

Posted: Sat Jun 22, 2013 4:06 pm Post subject: 


In a Feistel cipher, the encryption algorithm designer decides what permutations are to be made. All permutations are fixed (i.e., decided at algorithm definition time). The key doesn't affect these at all. An interesting historical fact about DES is that the initial and final permutations add no security at all. They were intentionally added to make software implementations of DES perform poorly. You see, permutation in hardware is a zero (time and implementation) cost feature: just hook the wires up in the prescribed order.
 John _________________ I can confirm that I have received between 0 and 499 National Security Letters. 

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dE_logics Advocate
Joined: 02 Jan 2009 Posts: 2253 Location: $TERM

Posted: Sat Jun 22, 2013 4:15 pm Post subject: 


Funny facts. It did not improve encryption, but it surly made the concept encrypted.
Thanks a LOT for the clarification. This bit was missing from all text on the Internet. Hope this post will help others. _________________ My blog 

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